The greatest singer on Broadway today is Katrina Lenk, and the greatest song written for the stage in decades is “Omar Sharif” by David Yazbek, which she sings in “The Band’s Visit.”

Lenk is on a roll, having come off a long run in “Indecent” and now moving with “The Band’s Visit” from Off-Broadway to the Ethel Barrymore Theatre.

“Omar Sharif” tells the story of how Dina, the owner of a small café in a back-of-beyond Israeli desert town, became entranced with those two Egyptian cultural icons, one a singer and one a movie star.

She sings the song to the leader of an Egyptian police orchestra which ended up in the wrong town and has to spend the night there. As she sings, she realizes she has deep feelings for the conductor, played by Monk’s Tony Shalhoub, making his debut in the world of Broadway musicals.

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“Omar Sharif” is haunting, lyrical, surprising, and hypnotic as a desert wind.

Lenk took some time between performances to describe her experience singing a piece destined to be a classic.

MICHAEL LEVIN: When you were auditioning, did they give you sheet music or an audio file?

KATRINA LENK: They gave me the sheet music.

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Did you say to yourself, “How am I going to sing this?” Or did you just automatically fall in love with it and know how you’d sing it?

I think every time I look at anything, I think, “Oh my God, how am I going to sing this?” It was both of those things. I was curious at how to do it and also very much wanting to do it. I was just very much in love with the song and also puzzled by it.

Puzzled how?

It has this deceptive simplicity to it. It seems like, oh yeah, this should be really easy. But the phrasing is quite long, and it has a pretty big range from bottom to top in the song, and the dynamic ranges are broad. There’s a lot going on that seems simple but isn’t. I was very much looking forward to learning it and working on it. I went to the audition and decided, even if I never get to sing this song again, I’m totally keeping the music because I loved it so much.

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At the end of each verse, there’s a downward scoop of six notes that the listener never expects. Did that surprise you?

The composition style was definitely influenced by Arabic music. I’m just only still a novice at knowing that style, but it’s circular and there are very long phrases and that’s what’s valued in that kind of composition. It’s very different than what is valued in Western style pop music. So I would bet that it seems like crazy long phrases to us, but it makes sense when writing in that idiom.

When you begin to sing “Omar Sharif,” it’s almost like you’re thinking out loud.

Katrina Lenk

(Jemal Countess/Getty Images for American Theatr)

That’s exactly it! Dina’s working through a big idea in her head that she may never have really crystalized before. I don’t think she’s ever really spoken to anybody about this particular feeling, or that she’s even really ever thought about it herself before.

You never seem to be efforting when you’re singing.

A lot of it feels very so close to speech. So it just feels like you’re taking a breath to speak something, and it just happens to be in this rhythm and on these pitches…but it doesn’t seem far away from how you would speak. That’s why I say the song is deceptively simple.

At the start of the play, Dina is simply offering the stranded Egyptians hospitality. At what point does she decide that she’s interested in something more from him?

Well, it’s never entirely set. It’s got some fluidity, so I can’t say for certain that it’s at this point or it’s at this point, because it just depends on the day. I would say when she finds out that he’s not just some straightlaced nerdy man who just plays oompa oompa music in the band, but he has this soul and he clearly understands what she means about culture. That’s when she becomes interested. It’s a gradual process of thawing.

It shows the connecting power of art and storytelling. It’s a movie that these two people are connecting over. But it meant so much to both of them in a similar way in different places and I love that. It’s a reminder that music and art are really important human connecting tools. It seems cliché to say it but I think it’s good to be reminded of it.

How do you protect your voice? How do you take care of yourself?

I’m still learning that one. It’s a lot of being boring. It’s not going out too much. It’s the talking — not so much the singing but how you use your voice when you’re not on stage.

Is performing the show as much fun as I think it is when you’re doing it?

Yes, and fun in the way like when you worked really hard at something. Because it was a puzzle — how do we make sure that the jokes get across and still sing it in a way that feels natural and not do too much. It was a lot of work and a puzzle in trying to figure things out. Yes, it’s a pleasure in all the ways that a hard-won pleasure can be.

I think that you made something that’s really, really hard look deceptively simple.